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<p>In this paper, a characterization of the invariant subspaces for idempotents on a Hilbert space is established. The problems when two orthogonal projections have a finite dimensional common invariant subspace and when an idempotent has a finite dimensional reducing subspace are also treated.</p>

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On invariant subspaces for idempotents

  • 期刊论文

  • 发表日期：

    2025年6月5日

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  • Xiao-Ming Xu,
  • Mi Yan,
  • Yuan Li

摘要

In this paper, a characterization of the invariant subspaces for idempotents on a Hilbert space is established. The problems when two orthogonal projections have a finite dimensional common invariant subspace and when an idempotent has a finite dimensional reducing subspace are also treated.